Alternative Proof of Gauss Integral with improper integral

[IshiguroYoshihiro]

Motivation for this change

I added an alternative proof of gauss integral and placed it in theories/showcase.
This is an experimental approach of improper integral.
The difference of proof strategy is that this version mainly relies on lemmas related to integration over unbounded intervals.

[NB(rei): this is the continuation of PR #1584 ]

Checklist

• added corresponding entries in CHANGELOG_UNRELEASED.md

• added corresponding documentation in the headers

Reference: How to document

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